Aristotle's wheel paradox

[Jonathan]

3 hours ago, Jon Letendre said:

Jonathan: “The above is reality, Tony. It proves your position false. What should you do now that you've been confronted with such overwhelming reality? What does the Objectivist philosophy advocate that you do?”

 

I can answer that, Jonathan. I can only speak for myself, so I will.

I hated The Romantic Manifesto. I just looked for it on my shelves. I don’t have it. (I have five nice copies of the original paperback of The Virtue of Selfishness, one of them the first printing, but no Manifestos.)

I was about 16. Had been reading her since about age 12 (VOS.) I couldn’t believe my eyes. I was so disappointed. It was all gibberish. Perfectly worthless blah, blah, blah. And all about a subject that mattered shit to nothing.

“This is pretty, that isn’t!”  What the fuck!

”And it deeply, deeply matters!” Oh, does it? Fuck the lord - what was going on? 

 I knew she was still very smart and that much of her philosophy had merit, but nevertheless I was going to have to get used to the idea that she had a penchant for blah blah gibberish, because she plainly did.

Years later I encountered other people (not Objectivists) arguing about art. Gibberish. Claiming to see all these things that simply are not there. (Things that aren’t anywhere!) But I noticed that they were making sense to each other. They disagreed with one another, but seemed to understand each other. I knew them to be smart people in several areas. Some of them I knew disagreed in other areas, but they agreed on their gibberish about art.

I had a choice. Either Rand and these smart people in my life were faking gibberish talkers or I did not see or live the things they saw and lived. I was already confident of the latter and that it went both ways anyway, so I chose the latter.

So then, you ask: What did the Objectivist philosophy advocate that I do?

—> Keep my mouth shut about art.

I've seen you discuss art. You have a rare mindset for someone posting in an O forum. You state what you experience, you don't try to deny that others experience what they say they do, and you don't pose as an authority. You don't impose your own limitations on others, and you don't feel attacked and insulted if someone might be more into it than you are or more knowledgeable. Really cool. Grown up, rational, not driven by emotions or dedication to St. Ayn's ex cathedra pronouncements.

J

[Jonathan]

Speaking of art and O-land, many Rand-followers share Tony's visual deficiencies, though to different degrees. They are not visually/mechanically competent, but they don't recognize that fact, and instead believe themselves to be the standard and limit of visual cognition. They set themselves up as the universal standard in determining what all humans are capable of experiencing. Antything beyond their own personal cognitive abilities is claimed to be a scam and a con job.

That is the history of the Objectivist Esthetics and its advocacy in a nutshell.

J

[anthony]

20 hours ago, Michael Stuart Kelly said:

Tony,

Who suggested the track and who slipped it in to attract and/or trap people?

Who set the trap?

Aristotle? 

 

Well, yes he did. Only, I don't think his intention was to deceive people.

OK, Max said it a few posts above and it looks like I'm squatting on his post, it, but still... If you think you have won something over all others, don't forget, you won over Aristotle, also. Right?

But this is not a competition. It's epistemology.

The problem in the disagreements is not recognizing reality, though. Both sides do. The problem is staking a claim to the One True Truth on visual representation, then claiming the other side does not see reality because they are referencing a different situation. However, what both sides are seeing is reality, just not the same set of real referents the other is seeing.

Open any dictionary and you will find at least two definitions for all words. The same goes for visual representations when they are ambiguous. Liberal (a symbol that we call a word) means freedom lover and big government advocate. Or with languages, chair in English and cadeira in Portuguese refer to the same thing. Which is the One True Truth in connecting referent to symbol? (Psssst... the Objectivist way of determining that is correctly identifying "context," then going the percept to concept route.  )

As to visual ambiguity, it's easy to show how the mind can trick us. Different parts of the brain process differently the initial electro-chemical signals the eye transforms photons into. Sometimes the seams are rough between those different parts of the brain, they don't communicate with each other well, but they communicate well with the command center, so to speak. Then we get visual paradoxes and illusions or even the inability to hold one interpretation of a visual representation in our awareness without it flipping to another interpretation (and in those cases, it keeps going back and forth).

The reason I'm saying this is that we all have brains that work in the same manner. When a difference in representation is subtle because the symbol is ambiguous, it's reasonable for some people to favor one interpretation over another. Both are true in the case of the wheel paradox, just not at the same time, as I keep saying.

Here's some proof about visual paradoxes and illusions due to the way the brain processes them.

Take a look at the images below. In the first, are the two middle circles the same size or is the left smaller than the right? Measure them and you discover they are the same size.

Below left, is it a sax player or a woman's face? After you decide on one, try to keep it in mind without seeing the other. You can't. If flips back and forth. Ditto for the image on the right below. Is it a goblet or two faces looking at each other? There are a ton of these things out there.

So which alternative is the One True Truth? All three images obviously represent something in reality. They are symbols that refer to concepts that refer to something in reality. Yet they seem to refer to different things at the same time. (Ditto for the diagram of the wheel paradox.)

Another point. You keep talking about an automobile tire for Aristole's wheel paradox, but you must be aware that automobiles didn't exist at the time Aristotle was alive. Right? Would it be correct for me to say I've debunked your argument because it was premised on an anachronism as concerns reality?

   

That's kinda like the way you are coming off in insisting the wheel paradox can only refer to the context and referents you assign--none others, that all other contexts and referents are false. What's more, you express satisfaction in a belief that you think better than others because of this insistence.  

But here's the thing. I don't mind your perspective because it's one of the true ways to interpret the diagram. Everybody agrees that the object you are talking about exists in reality. Everybody. But other things exist, too, and I demand the right to assign any conceptual referent to any symbol I please. I demand it, I say! You will not determine the referent content of the symbols in my skull! Begone invader!  

Oddly enough, even when Jonathan or Jon show you images and videos of something in reality, something as real as an automobile tire, things like stone wheels and bicycle chains, you refuse to admit they exist. Why?

They exist.

And presuming they exist, after all, we can see them and the photographers can touch them, feel them, taste them, and even hear them if they move and make noise, then by default they are reality referents that can be assigned to a visual symbol that stands for a concept, yet you deny that is possible.

For that matter, the two wheels stuck together as in the way you keep portraying exist, too. And this works the same way. You can assign the object made of two wheels to a visual symbol that stands for a concept.

So why does a tire exist for you and a bicycle chain not?

The only thing I can think of is primacy of the visual symbol, i.e., primacy of consciousness.

So which takes primacy for you, a visual symbol or the things in reality to which a symbol (or a word) can refer?

If reality is primary for you, then you have to admit objects in reality exist (or allow them to exist if you are in God mode  )in all their variety and different contexts. Like roads, for instance...

 

Michael

13

Michael : I can only restate my argument. "Reality" is not (per se) an experimental demonstration *about* a wheel - reality is the wheel itself, in the concrete and in the identity of all wheels - and how one views AND abstracts it. I've tried to say a few times, that *no matter* what the Paradox poses, we, all of us, have as final referent to compare with, what we know of the actual existence of the wheel. A "set up", e.g. of the 'paradox', diagram and information given, is second-hand, so to speak, and man-made, so can sometimes have been manipulated or fallacious.

It must not be taken as a literal and authoritative reproduction of what a wheel does--not until one understands the paradox and knows that this wheel behavior is true to reality--therefore no paradox. Isolate the diagram, etc. from reality, and we get the kind of rationalism seen. Isolate it from one's abstractive mind and see the skepticism.

After, can come all the experiments one wants. On that score, a video-ed demo of an experiment will often lack context and be meaningless; it can be badly set up; it can be deliberately falsified; it can be innocently erroneous.

When I said that I can make a bottle do whatever I want, I meant it. If I want, I can make it skid/slip off to either side - or I can make it run straight, without slippage. (Which is what it always does, rolling alone without a second support).

I performed this for myself, to test what I already knew from experience. I knew in advance in my mind, what would be needed to make the bottle perform any of those actions. (Minute adjustments e.g., to the alignment of  levels of the two surfaces carrying neck and bottle, achieved any outcome I wished).

The credulousness heard here about the Final Authority of this video or that 'experiment', actually amazes me.

To be adept at photography requires, to mention only two skills: regularly lengthy practice at arranging and playing with experiments of the placement of objects; and also a  'pre-visualization' technique - 'seeing' in advance of doing anything, what an arrangement - and the final image - will look like. After 45 years at this, I can claim some skill at both.

An experiment is very much (also) "a re-creation of reality". The "physicalists" (as I call them) or skeptics of conceptual reasoning, around these parts could do well to comprehend the difference.

All in all, it is not how one, or I, interpret the diagram - it completely involves what a wheel is. Otherwise it becomes a rather meaningless mind-game. I have heard nothing which invalidates what is obvious (and many won't admit knowing) - the little wheel goes where the large wheel goes. Simply. I've established that enough times. An extra "track" is superfluous when you can properly see any wheel in action. Anyone care to honestly debate that?  

Michael, I must add: I have done nothing- but -argue against the "primacy of the visual symbol". Now and before. That is the "trap" I detect here.

 

[Jonathan]

4 minutes ago, anthony said:

 "Reality" is not experimental demonstration *about* a wheel - reality is the wheel itself and how one views AND abstracts it.

And you are incapable of viewing and abstracting what's happening with the wheels in the so-called "paradox."

You're impaired.

You're like a blind man refusing to believe that he's blind, and refusing to believe that others can see.

 

7 minutes ago, anthony said:

It must not be taken as a literal and authoritative reproduction of what a wheel does--not until one understands the paradox...

You don't understand it.

 

8 minutes ago, anthony said:

Isolate the diagram, etc. from reality, and we get the kind of rationalism seen.

I agree. The ancient thinkers isolated the diagram from reality. The result was a lot of eggheaded stupidity. Merlin also isolates it from reality. Again, the result is stupidity. You, Tony, have followed Merlin in isolating the diagram from reality, and you've even gone so far as to obey him in eliminating items that the original setup included so that you can isolate the diagram even further from reality. The result, as always, has been stupidity.

 

12 minutes ago, anthony said:

After, can come all the experiments one wants. On that score, an experiment will often be meaningless; it can be badly set up; it can be deliberately falsified; it can be innocently erroneous.

I have no doubt that you are so incompetent at physical experimentation that you will easily fool yourself while believing that you had set up an experiment with great precision. You are naturally unaware and unobservant. That is your everyday mode of existence. It's not going to suddenly magically change because you're doing an experiment.

 

15 minutes ago, anthony said:

When I said that I can make a bottle do whatever I want, I meant it. If I want, I can make it skid and slip off to one side - or I can make it run straight, without slippage. (Which is what it does, alone).

 

No, you can't make it do those things. Reality doesn't conform to your whims. What's actually happening is that you don't have the slightest clue how to measure friction and slippage, etc. Your "methodology" is to just look at something in a state of ignorance, have feelings about it, and then believe that you've rigorously scientifically tested it. "I dint see no slippage! So there aint none!"

 

18 minutes ago, anthony said:

I only tested this out for myself, to confirm the fact. I knew in advance in my mind, what would be needed to make the bottle perform any of those action. (Minute adjustments e.g., to the levels of the two surfaces, will achieve any outcome I wish).

False. You didn't know what would be needed to make the bottle perform any actions, and you still don't know. You haven't the slightest clue.

 

19 minutes ago, anthony said:

The credulousness heard here about the Final Authority of this video or that 'experiment', actually amazes me.

Yeah, here you're drifting into your standard dodge, which is a combination of attacking straw men and Randsplaining.

 

20 minutes ago, anthony said:

To be adept at photography requires, to mention only two skills: huge amounts of arrangements and experiments of placement of objects; and also a practised 'pre-visualization' - 'seeing' in advance what an arrangement - and the final image - will look like. After 45 years at this, I can claim some skill at both.

Bullshit. I've known many, many photographers who are visuospatially/mechanically deficient. There is a massive difference between a photojournalist composing a scene and a mechanical engineer properly envisioning the workings of moving parts. Your ability to handle the former does not translate to your being able to do the latter. You've failed miserably in regard to this "paradox." You've demonstrated your incompetence. Saying, "But, hey, I was a photographer, so that proves that I gots the vision powers," is pathetic, and doesn't cancel the ineptitude that you've displayed, live, right here in front of us.

The "Aristotle's Wheel Paradox" is very effective, compact little test of visuospatial/mechanical reasoning abilities. You've failed it. And beyond that, you've failed not just in answering the question, but in understanding the question.

 

31 minutes ago, anthony said:

An experiment is very much (also) "a re-creation of reality". The "physicalists" (as I call them) or skeptics of conceptual reasoning around these parts could do well to comprehend the difference.

We're not "skeptics of conceptual reasoning." We're critics of YOUR RETARDED reasoning. Heh. Don't try to pretend that, since we're criticizing your erroneous thinking, that we're therefore criticizing all thinking. Really lame tactic there, Tony.

J

 

[anthony]

 

There is an excess of drift, consensus and presumed premises. Begin at the beginning. It is about time all here "restate" the 'paradox' in your own words. Then, explain your solutions, simply.

[Jonathan]

1 minute ago, anthony said:

 

There is an excess of drift, consensus and presumed premises. Begin at the beginning. It is about time all here "restate" the 'paradox' in your own words. Then, explain your solutions, simply.

Jon has been asking you to do that for several pages now.

Before you do, please read the original formulation in the Mechanica:

 

Quote

 

In antiquity[edit]

In antiquity, the wheel problem was described in the Aristotelian Mechanica, as well as in the Mechanica of Hero of Alexandria.^[1] In the former it appears as "Problem 24", where the description of the wheel is given as follows.

For let there be a larger circle ΔZΓ a smaller EHB, and A at the centre of both; let ZI be the line which the greater unrolls on its own, and HK that which the smaller unrolls on its own, equal to ZΛ. When I move the smaller circle, I move the same centre, that is A; let the larger be attached to it. When AB becomes perpendicular to HK, at the same time AΓ becomes perpendicular to ZΛ, so that it will always have completed an equal distance, namely HK for the circumference HB, and ZΛ for ZΓ. If the quarter unrolls an equal distance, it is clear that the whole circle will unroll an equal distance to the whole circle, so that when the line BH comes to K, the circumference ZΓ will be ZΛ, and the whole circle will be unrolled. In the same way, when I move the large circle, fitting the small one to it, their centre being the same, AB will be perpendicular and at right angles simultaneously with AΓ, the latter to ZI, the former to HΘ. So that, when the one will have completed a line equal to HΘ, and the other to ZI, and ZA becomes again perpendicular to ZΛ, and HA to HK, so that they will be as in the beginning at Θ and I.^[2]

The problem is then stated:

Now since there is no stopping of the greater for the smaller so that it [the greater] remains for an interval of time at the same point, and since the smaller does not leap over any point, it is strange that the greater traverses a path equal to that of the smaller, and again that the smaller traverses a path equal to that of the larger. Furthermore, it is remarkable that, though in each case there is only one movement, the center that is moved in one case rolls a great distance and in the other a smaller distance.^[1]

-----

 

 

Tony, do you see the parts about the wheels rolling? Look again. Specifically look for the words "unroll" and "roll."

Then, before yapping some more, go back and look one more time.

J

 

[anthony]

"it is strange that the greater traverses a path equal to that of the smaller, and again that the smaller traverses a path equal to that of the larger. Furthermore, it is remarkable [...]

What I said six-plus times, in my own words. Now you all do the same.

"Strange". "Remarkable".

Nowhere: "impossible". Nowhere: 'this must be fixed''. (Extra track, slippage - blah).

Aristotle apparently had too much respect for what IS: identify the reality. This is all that is indicated above.

[Jonathan]

Hey, 'member back when Merlin posted this link to the video that he though was very helpful?

On 9/13/2017 at 5:43 AM, merjet said:

I found this video very helpful for thinking about the paradox. More hands-on is a roll of tape.

Heh. The nice thing is that it's not Wikipedia, and therefore Merlin can't meddle with it!

Anyway, it's fun going back to that old video that Merlin endorses, and to revisit taking a closer look, frame by frame.

For example, check this out:

As the circles leave their starting points (white dots on the black lines in this video), notice what happens! See the difference in distance already covered by the point on the smaller wheel?

<Gasp!> Tony, can you see it?

The same happens as the circles near the finish line.

What does it mean, Tony?!!!! Merlin?!!!!

Is it a hawgwarsh crutch?

Heh.

J

[Jonathan]

16 minutes ago, anthony said:

"it is strange that the greater traverses a path equal to that of the smaller, and again that the smaller traverses a path equal to that of the larger. Furthermore, it is remarkable [...]

What I said six-plus times, in my own words. Now you all do the same.

"Strange". "Remarkable".

Nowhere: "impossible". Nowhere: 'this must be fixed''. (Extra track, slippage - blah).

Aristotle apparently had too much respect for what IS: identify the reality. This is all that is indicated above.

You missed what I told you to look for, Tony. You edited it out.

Go back and look again.

Reality doesn't go away when you blank it out. Wishing reality away doesn't work.

Go back and look again. Look for the words "unroll" and "roll."

J

[anthony]

9 minutes ago, Jonathan said:

Hey, 'member back when Merlin posted this link to the video that he though was very helpful?

Heh. The nice thing is that it's not Wikipedia, and therefore Merlin can't meddle with it!

Anyway, it's fun going back to that old video that Merlins endorses, and to revisit taking a closer look, frame by frame.

For example, check this out:

As the circles leave their starting points (white dots on the black lines in this video), notice what happens! See the difference in distance already covered by the point on the smaller wheel?

<Gasp!> Tony, can you see it?

The same happens as the circles near the finish line.

What does it mean, Tony?!!!! Merlin?!!!!

Is it a hawgwarsh crutch?

Heh.

J

Good, it confirms what I also kept repeating, the circles rotate at different speeds since the circumferences are different.

You're running on empty, lad.

[Jonathan]

27 minutes ago, anthony said:

Good, it confirms what I also kept repeating, the circles rotate at different speeds since the circumferences are different.

You're running on empty, lad.

You're not even paying attention to or grasping your own argument.

Your position was that the larger circle moves at a faster speed. In the image that I posted, the point on the smaller circle has moved out faster. That's the opposite of your position.

You're so unaware and unobservant, and such a sloppy thinker, that you believe that you find confirmation in the opposite of your position!

Hahahaha!

J

[Michael Stuart Kelly]

2 hours ago, anthony said:

Michael : I can only restate my argument.

Tony,

So you are not going to consider the things--the reality things--I talked about? 

No problem.

I'm not offended. It's your mind.

Some people don't want to think about certain things and others do.

Since you don't, I'll stop talking about it with you.

It's still a good life with good people in it. And you are one of those.

 

Michael

[anthony]

5 hours ago, Michael Stuart Kelly said:

Tony,

So you are not going to consider the things--the reality things--I talked about? 

No problem.

I'm not offended. It's your mind.

Some people don't want to think about certain things and others do.

Since you don't, I'll stop talking about it with you.

It's still a good life with good people in it. And you are one of those.

 

Michael

Michael, Why do I have the feeling you switched off after my opening words?  Also, I have no restrictions on what I consider, it is all grist to my mill.

If you read carefully you'd see I applied my reply to what you said. If not always, directly. (About "visual ambiguity", right, OK. I've seen and read some on pictorial illusions. (The paradox isn't one).

Your last two or three paragraphs up above, in fact, are in agreement with what I'm saying, throughout.

Then: "They exist", (apropos of videos etc). "You refuse to admit they exist".

But I do.  I just reject the validity of a "track solution" which they try to prove. I "admit" anything my eyes inform me. I often have not accepted, with normal skepticism, what I'm being told these, and many things I am showed in life, are supposed to MEAN. That's the critical difference.  And like any diagram and picture, they don't necessarily depict the reality of a wheel. A photograph never lies, they say? I know they can and do. Long before Photoshop, as well.

 I depend on my personal familiarity with and thinking of "the wheel', much more. One has to know the difference between a setup and the object of the setup. Some individual's mind interposed itself in the making of it (like art).

And I'm the main one who will bring in the auto tyre and any other examples of 'wheel/circle' as comparison. Also I explained what can go wrong with an experiment. (I've worked in a lab too).

I can go on and on making my point (and explicitly, Aristotle's, I read recently) that the observable REALITY of a wheel in a wheel, is that it "traverses a path equal to the larger". (In 'apparent' contradiction to their circumferences). Nobody can refuse to see this. There is the 'paradox' that isn't. Here is the 'what?' to be accepted (obeyed) - then, understanding the science of the how and the why, can and will follow. One can't change the 'what?'. Therefore, inventing 'tracks" and such - in order to solve the 'paradox' - is redundant, at least, and primacy of consciousness, at worst.

There are not two possible ways of seeing this 'paradox'. I think it is self-evident and self-explanatory, and one is correct, the other wrong. Always, must the "wheel" (and one's mind) take precedence over any representation of it. 

[Jonathan]

22 minutes ago, anthony said:

Michael, Why do I have the feeling you switched off after my opening words?  Also, I have no restrictions on what I consider, it is all grist to my mill.

If you read carefully you'd see I applied my reply to what you said. If not always, directly. (About "visual ambiguity", right, OK. I've seen and read some on pictorial illusions. (The paradox isn't one).

Your last two or three paragraphs up above, in fact, are in agreement with what I'm saying, throughout.

Then: "They exist", (apropos of videos etc). "You refuse to admit they exist".

But I do.  I just reject the validity of a "track solution" which they try to prove. I "admit" anything my eyes inform me. I often have not accepted, with normal skepticism, what I'm being told these, and many things in life, are supposed to MEAN. That's the difference.  And like any diagram and picture, they don't necessarily depict the reality of a wheel. A photograph never lies, they say? I assure you they can and do. Long before Photoshop, as well.

 I depend on my personal familiarity with and thinking of "the wheel', much more. One has to know the difference between a setup and the object of the setup. Someone's mind interposed itself in the making of it (like art).

And I'm the main one who will bring in the auto tyre and any other examples of 'wheel - circle'. And I explained what can go wrong with an experiment, too. (I've worked in a lab too).

I can go on and on making my point (and explicitly, Aristotle's, I read recently) that the observable REALITY of a wheel in a wheel, is that it "traverses a path equal to the larger". Nobody can refute this. That is the 'paradox' that isn't. Here is the 'what?' to be accepted (obeyed) - then, understanding the science of the how and the why, can and will follow. You can't change the 'what?'. Therefore, inventing 'tracks" and such - in order to solve the 'paradox' - is redundant, at least, and primacy of consciousness, at worst.

There are not two possible ways of seeing this 'paradox'. It is self-explanatory. One is correct, the other wrong. Always, must the "wheel" take precedence over any representation of it. 

So, MSK was correct. Tony is "not going to consider the things--the reality things--[MSK] talked about."

He's going to cling instead to his false position that someone here at OL "invented" a "track" "in order to solve the 'paradox.'" He is not going to accept the reality that a track under each wheel was included in the original setup of the "paradox" in the Mechanica (the text, attributed to Aristotle, in which the wheels "paradox" appeared), and that the tracks are vital to the alleged "paradox."

Mind closed.

Heh. And he's going to continue blabbering on about his misinterpretations of the "paradox" and about the straw man positions that he is assigning to others.

In other words, standard, typical Tony.

J

[anthony]

6 hours ago, Jonathan said:

You're not even paying attention to or grasping your own argument.

Your position was that the larger circle moves at a faster speed. In the image that I posted, the point on the smaller circle has moved out faster. That's the opposite of your position.

You're so unaware and unobservant, and such a sloppy thinker, that you believe that you find confirmation in the opposite of your position!

Hahahaha!

J

Pff. Anyone can see the point on the large circle arriving before the inner one, but starting and ending points are not an accurate indication. It's the *average* speeds of each through the whole cycle that only matters. Average velocities can be calculated easily. Circumference (distance) divided by time duration. But I'm going to be told that -  despite everything seen and everything known - the small one rotates faster!? Wow.

[Michael Stuart Kelly]

1 hour ago, anthony said:

Michael, Why do I have the feeling you switched off after my opening words?  

Tony,

You should learn to think with your mind, not just your feelings.

   

(That's just a quip...  )

I read your entire post. It may come as a shock to you, but I read every word of your post--all of it--and still hold to my views. So it's not that I disagree with you because I didn't read what you wrote, it's that I did read your words and they reinforced my reasons for disagreeing.

 

To be precise, I disagree with several of your conclusions and agree with others. But I'm not going to go into that (actually I already did on a lot of them) because you totally ignored what I said. So what's there to discuss? You won't address the issues I raise, but just keep repeating things you've said a million times already on this thread.

I am not swayed by argument by repetition. There has to be logic, conceptual content, standards, definitions, correct identifications, context, etc. etc. etc.

Repeating doesn't do that. Ignoring issues brought up doesn't do that. Oh, you presented some of such things in your repetitions, but only some. And the elements you did present were already there from your first comments. You won't even look at the other stuff that needs reasoning--you just dismiss it outright. So substance-wise, that kind of repetition communicates this: "You're wrong you're wrong you're wrong you're wrong you're wrong you're wrong you're wrong you're wrong..." graaaaak! Polly wanna cracker...  

That means, according to my own standards, there's nothing to discuss. I'll discuss this issue with people who want to discuss it. I actually learned something I didn't know before by doing precisely that on this very thread. I worked through an idea with a little help from those who knew more than I did and now I have more knowledge than before. (Yay me.  And thank you to them.  )

You have communicated--and communicated well--that you have no need for this knowledge and no wish for it. What's more, you don't even believe it's knowledge and think those who do are dummies. OK. I am perfectly fine with that decision.

I only made a long post before to you because I thought you were interested for real in understanding this issue and, having recently worked my own way through it, thought I could shed a little light on where the blind spots were. After all, I experienced them myself right here on this thread before checking my premises and you have the same ones I had. But so far, you only show interest in repeating what you do know of the wheel paradox issue and only doing that. Result: waste of time for everyone. My mistake.

We don't have to have the same wants and needs and we certainly don't have to agree on everything to be friends.

So I hold--and will always hold--you are one of the good ones. I mean that. We're merely at cross purposes on this one issue (we seek different things from it) and it's no real biggie in the context of our respective lives. We just leave that out when we talk to each other and it's all good.

And even if we do talk about it some more and still run into a Mexican standoff, who cares? It certainly won't affect my good opinion of you. I mean, I used to be a crack addict. And I consider myself a good person, even back then (except when I did some things I am not proud of  ). The point is, I got out of it and that's mostly because, deep inside, I was and am a good person. So my bar is really high to change my good opinion of someone. It's higher than a wheel paradox, I can tell you that.

 

Michael

[Jonathan]

1 hour ago, anthony said:

Pff. Anyone can see the point on the large circle arriving before the inner one, but starting and ending points are not an accurate indication. It's the *average* speeds of each through the whole cycle that only matters. Average velocities can be calculated easily. Circumference (distance) divided by time duration. But I'm going to be told that -  despite everything seen and everything known - the small one rotates faster!? Wow.

Heh. So, now your theory is that the smaller wheel starts our faster than the larger wheel,  but then slows down somewhere during the middle of the trip, and then speeds up again right at the end? And therefore the relative accelerations and declarations of both wheels have to be averaged in order to arrive at the truth? The wheels know where the start and finish lines are, and choose to behave differently when near them? Your little theory is that the image that I posted, of the smaller wheel's point covering more territory faster than the larger wheel's point, would not be true of any paired points on the large and small wheels during any and every moment of the cycle, but it is only true at the start and finish lines?

Buffoon.

J

[merjet]

On 11/23/2018 at 1:10 PM, Max said:

Applying the same argument to the large circle: every cycloid of the large circle (cycloid length = 8*R) is greater than 2*pi*R . Therefore, the large circle rolls farther than it would by pure rolling? You've created a new paradox!

. . . .

At least I'm not the one who is drowning.

Duh! Your analogy fails, since you misunderstood the argument.

P1. The smaller circle rolls further horizontally 2*pi*R.

P2. It would roll horizontally 2*pi*r by pure rolling separately.

P3. 2*pi*R > 2*pi*r

P1, P2, and P3 are all about straight lines, i.e. translation vectors. P1 is not about a cycloid the way you botched it. That is your fallacy.

. . . .

You got that backwards. You’re helpless with your crutch snatched away by whitewater.  

. . . .

“But he doesn’t find that, as his cycloid argument is fallacious (see above). It is really worse than you think" (link).

It is not fallacious. The fallacy is your analogy (see above). The alleged “new paradox” is your fabrication.

 

[merjet]

On 11/23/2018 at 1:43 PM, Max said:

[1] That those cycloids are completely superfluous, you show yourself in your second “solution”, in which no cycloid at all is mentioned.

[2] Better even, look at the previous link you gave yourself: click on “summary” and scroll down to “rolling and slipping”: those guys don’t make a distinction between slipping and skidding either, they call it all “slipping” positive or negative. And they don't put "slipping" between scare quotes! In a link that you recommend!

[3] Ever seen a train wheel? 

[4] It is not a crutch ... …. “Whether such a surface exists in reality (it does for train wheels) is irrelevant.”

[5] That “because” here is nonsense.

[1] They are two different solutions, both sound. They use different methods. The second solution is based on only comparing the before and after positions using translation in physics expressed in Cartesian coordinates for every starting point (x,y) of the larger circle and every point within it.

(x,y)  (x + Δ x, y + Δ y)       Δ x = 2*pi*R for every (x,y)       Δ y = 0 for every (x,y) 

The cycloids are “omitted measurements.” Said translations hold for many possible transitions between start and end. Which particular one doesn’t matter.

The first solution considers the before and after positions and the transition. The transitions of points are cycloid shaped. The cycloids are not “omitted measurements.”

[2] Duh! They say nothing about inner circles slipping either. When they use slipping, it’s about the whole wheel! They don’t use crutches to fake reality either. Unlike you and the two idiotic, hysterical jackasses do!

[3] You’re not very observant. Link.

[4] It is a crutch. So you think that reality is irrelevant.

[5] Nonsense.

[merjet]

On 11/24/2018 at 6:32 AM, Max said:

I don't understand that. I see no difference between "the second wheel is along for the ride" and "two wheels stuck together". In both representations there is only one rigid object, that consists of two wheels with a common center. The only difference in interpretation would be either to treat those wheels as a mechanical system or to treat the paradox as a mathematical problem, but as I've shown in earlier posts, the two descriptions are equivalent. 

 

On 11/24/2018 at 6:50 AM, Max said:

From the original version of the Wikipedia article: "The wheels roll without slipping for a full revolution." Rolling wheels, you know. No doubt chosen by Aristotle while it is rather natural for wheels to roll and to slip or not to slip, in contrast to rings of an archery target. Does the fact that rolling and slipping of archery target rings is a rather silly notion imply that rolling and slipping of car wheels or train wheels is ridiculous?

Also, here and here.

Heh. A dogmatist – and like a propaganda agent from Nineteen Eighty-Four’s Ministry of Truth -- chants his mantra again, while blanking out reality as follows.

- It is Aristotle’s wheel paradox, not Aristotle’s wheels paradox.

- The ‘Wrong problem entirely’ section of the Wikipedia Talk page

- The problem as posed for the first time in Mechanica is about two circles, not two wheels.

Also, the journal article ‘Aristotle's Wheel: Notes on the History of a Paradox’ by Israel E. Drabkin, which is referenced 6 times (!) in the Wikipedia Article includes the following:  “For though the smaller circle traverses a distance equal to that traversed by the larger, it does not keep pace with the larger by sliding over the tangent, if by ‘sliding’ we mean that a point on the circumference is at any time in contact with a finite segment of the tangent” [my bold].

The article throughout concerns one wheel, two circles.

The term two wheels that was in the Wikipedia article was put there by somebody with a poor understanding of the history. It has duped several readers, even though Wikipedia had a prominent warning at the top of the page saying the article is factually disputed. Ignoring the warning and swallowing whole what was written was imprudent.

 

 

[merjet]

On 11/23/2018 at 1:36 PM, Jon Letendre said:

Wheels roll on ceilings? In which direction do they rotate to pull that off?

If the opportunity comes, I’ll nominate those for a hall of fame for stupid questions.

[merjet]

On 11/24/2018 at 11:34 AM, Jonathan said:

???

Dipshit, I haven't used the word "molesting" on this thread. Dig your senile head out of you ass and try to pay attention to who has actually said what.

The nitpicking ankle biter, obnoxious ignoranus, reality-faking (link), lying, incompetent, hysterical jackass wrote: “I haven't used the word "molesting" on this thread.”

So you are saying I did not molest Wikipedia and you are calling Jon a liar. 

Beep-beep. Vroom.

Nitpicking idiot, you have arbitrarily and dishonestly accused me of dishonestly editing, messing with, and polluting the Wikipedia article, and “fucking with it” (link). You might fool yourself into believing your accusations don’t amount to molesting, but you don’t fool me and your dishonesty is in plain sight.

 

 

[merjet]

On 11/24/2018 at 12:07 PM, Jonathan said:

I've witnessed some Dunning-Kruger Effect stupidity out there in everyday life, but it's not even close to what you get here (not Objectivist Living per se, but all of Objectivist-land). Its astounding.

J

You are a perfect example of it. Beep-beep. Vroom.

[Jonathan]

20 minutes ago, merjet said:

The nitpicking ankle biter, obnoxious ignoranus, reality-faking (link), lying, incompetent, hysterical jackass wrote: “I haven't used the word "molesting" on this thread.”

So you are saying I did not molest Wikipedia and you are calling Jon a liar. 

Beep-beep. Vroom.

Non sequitur.

Non sequiturs aren't clever or funny zingers, if that's what you were thinking, gramps.

J

 

[merjet]

On 11/25/2018 at 10:34 AM, Max said:

That guy was that idiot Aristotle, who even didn't know the identity of the wheel! He was of course so stupid that he overlooked the internal logic of a wheel. It's clear that he must have never seen a wheel in his life.

Asinine.

P.S. https://en.wikipedia.org/wiki/Chariot#Greece